The setup: Lenny Bruce was not the first standup comedian, but he did create what we now mean by "standup comedy". The idea of some guy on a stage, often some guy with problems, who finds himself at odds with the establishment and has only his wits to resist with: that all begins with Bruce.

Whether he or the establishment won, of course, is another matter. Today, his assaults on censorship, racism, the Vietnam war and bigotry in general all occupy a triumphant place in the mainstream of western thought (if not always in western practice). At his death in 1966, however, the score was probably a tie.

Yet the film remains an apt monument in another way, not so much to what Bruce gave the world, but what it did to him. When it was recorded, he was in deep trouble with drugs, bankrupt from defending himself against obscenity charges, and banned from most of the nightclubs in the US, as well as all of Britain and Australia. He was world famous, and a complete mess.

Funny, how? Most of the big laughs in our lives come not from professional comedy, but from our family and friends, and that's what Bruce brought on to the stage. Even in this performance, as he leafs through court documents to share his outrage at the stupidity and unfairness he's been subjected to, he seems relaxed. He was famous (and will stay famous thanks to Don DeLillo) for his use of hepcat slang like "cool" and "chick" and "dig", but the words were only there because it's how he spoke. An early panning in Variety clearly thought it had found his weak spot when it said: "Mr Bruce is only trying to make the band laugh." In fact it was this abandonment of theatricality that made people love him.

And it was not an act. Bruce had "bits", of course – the bit about how to relax your "coloured friends" at parties became a favourite – but he discussed that openly, while between times he used to wander honestly around his feelings and ideas, as people do in conversation. He was also a master of accents and voices, which seem to bubble out of him almost uncontrollably at times. In this show alone, we hear from plantation slaves, Las Vegas wiseguys, Irish priests, even a Syrian, among countless others who are often just floating characters that come from God knows where.

Looseness has its price, of course. Bruce was known for his wavering coherence, which is certainly on show here. But the brilliance is on show as well – in his performance of walking in on Eleanor Roosevelt getting changed, or his story about the hooligan club-owner he once worked for – although artistically he has nothing to prove. The film is best watched as a reminder, not just of the man who made modern standup comedy, but of someone who helped to make a world that would allow it.